Main Question or Discussion Point

This is actually the formula for the specific heat of an Einstein solid, which is pretty easy to derive but I haven't been able to calculate the limit to show it becomes Dulong-Petit at hight temperatures. Maybe I've been missing something simple... I don't see how you could use l'Hopital's rule.

note: I wasn't sure whether I should post this in one of the physics forums, but I figured it's more of a calculus problem at this point.